To determine the level of temperature fluctuations \(\left\langle \theta ^2 \right\rangle \)  for large Péclet numbers, we need a model for the background turbulence, \(f_{ij}^{(0)}({k})\) .
We use statistically stationary density-stratified
compressible background turbulence,
which is determined by the following correlation
function \(f_{ij}^{(0)}({k})=\left\langle u_i({k}) \, u_j(-{k}) \right\rangle ^{(0)}\)  of the velocity field in the \({k}\)  space [1]}, [2]}, [3]}:
\(&& f_{ij}^{(0)}({k}) = {1 \over 8 \pi \, k^2 \, (1+ \sigma _c)} \,\biggl \lbrace E(k)\, \biggl [(\delta _{ij} - k_{ij}) \, \left(1 - {\lambda ^2 \over k^2}\right)\nonumber \\&& \quad + {\lambda ^2 \over k^2} \, \big (\delta _{ij} - \lambda _{ij}\big )\biggr ] + 2 \sigma _c \, E_c(k) \, k_{ij}\nonumber \\&& \quad + {{\rm i} \over k^2} \, \left[E(k) + \sigma _c \, E_c(k)\right] \, \big (k_j \lambda _i - k_i \lambda _j\big ) \biggr \rbrace  \left\langle {u}^2\right\rangle ,\) 
